Pre-Calculus: 1001 Practice Problems For Dummies (+ Free Online Practice). Mary Jane Sterling

      401. Jase is in a hot air balloon that is 600 feet above the ground, where they can see their brother Willie. The angle of depression from Jase’s line of sight to Willie is 25°. How far is Willie from the point on the ground directly below the hot air balloon?

      402. A bird is flying at a height of 36 feet and spots a windowsill 8 feet off the ground on which to perch. If the windowsill is at a 28° angle of depression from the bird, how far must the bird fly before it can land?

403. A submarine traveling 8 mph is descending at an angle of depression of 5°. How many minutes does the submarine take to reach a depth of 90 feet?

      404. You’re a block away from a building that is 820 feet tall. Your friend is between you and the building. The angle of elevation from your position to the top of the building is 42°. The angle of elevation from your friend’s position to the top of the building is 71°. To the nearest foot, how far are you from your friend?

      405. A lighthouse is located at the top of a hill 100 feet tall. From a point P on the ground, the angle of elevation to the top of the hill is 25°. From the same point P, the angle of elevation to the top of the lighthouse is 50°. How tall is the lighthouse?

      406. A surveyor needs to find the distance BC across a lake as part of a project to build a bridge. The distance from point A to point B is 250 feet. The measurement of angle A is 40°, and the measurement of angle B is 112°. What is the distance BC across the lake to the nearest foot?

      Illustration by Thomson Digital

Working with Special Right Triangles

       407−410 Find the length of the side indicated by x.

      407.

      Illustration by Thomson Digital

      408.

      Illustration by Thomson Digital

      409.

      Illustration by Thomson Digital

      410.

Illustration by Thomson Digital

Changing Radians to Degrees

       411−415 Convert the radian measure to degrees. Round any decimals to two places.

      411.

      412.

      413.

      414. 3

      415. 0.93

Changing Degrees to Radians

      416−420 Convert the degree measure to radians. Give the exact measure in terms of .

      416. 225°

      417. 60°

      418. −405°

      419. 36°

      420. 167°

Finding Angle Measures (in Degrees) in Standard Position

      421−422 The terminal side of an angle in standard position on the unit circle contains the given point. Give the degree measure of .

      421.

      422.

Determining Angle Measures (in Radians) in Standard Position

      423−425 The terminal side of an angle in standard position on the unit circle contains the given point. Give the radian measure of .

423.

      424.

      425.

Identifying Reference Angles

       426−430 Find the reference angle for the angle measure. (Recall that the quadrants in standard position are numbered counterclockwise, starting in the upper right-hand corner.)

      426. 167°

      427. 342°

      428. 265°

      429. 792°

      430. −748°

Determining Trig Functions by Using the Unit Circle

      431−434 Find the exact value of the trigonometric function. If any are not defined, write undefined.

      431. sin 225°

      432. tan 330°

      433. cos 405°

      434.

Calculating Trig Functions by Using Other Functions and Terminal Side Positions

       435−440 Use the given information to find the exact value of the trigonometric function.

      435. Given: ; is in quadrant I

      Find:

      436.